Field of the Invention
Embodiments of the invention relate generally to calibration and metrology apparatus, methods, and applications. More particularly, embodiments relate to apparatus and methods for calibrating actual parameters such as motion and distance, based on respective design parameters, and metrology, on the nanometer and sub-nanometer scale applied, for example but not limited to, inertial sensors such as accelerometers, grating accelerometers, compass sensors, and gyroscopes. Even more particularly, embodiments pertain to the incorporation and utilization of a modified Nano Optical Ruler Imaging System (NORIS) for said calibration and metrology apparatus and methods.
Description of the Related Art
Micro-machined accelerometers and gyroscopes have revolutionized motion sensing in the commercial world. They have also significantly penetrated the needs of the military for offering navigation for weapons and soldier/vehicle navigation. For most applications though, the sensors have to be complemented with GPS data to enable total inertial sensor based navigation capability. This is because the sensors suffer from biases and scale-factor variations from device to device, and over time. Furthermore, even if one could calibrate the devices after packaging, there are significant scale factor and bias drifts that render the initial calibration ineffective. These drifts occur due to thermally induced creep in packaging and device anchors, environmental vibrations, thermal expansion gradients, electronic noise, shock, and numerous other variables. In particular, when the sensors are placed in weapons which are ejected at high accelerations of >15,000 g, most inertial sensors develop significant bias drifts. Due to the large shocks, or temperature cycling, and the different thermal expansion coefficients of the package layers, stresses onto the small inertial sensors change over time, changing the sensor sensitivity and bias. One way to solve the sensor drift problem is to realize self-calibration techniques directly onto the sensor chip. If one could package a rate table with every sensor, the sensors could be calibrated on-demand. For example, after the sensors are ejected at high accelerations or subjected to repeated temperature cycling, the sensors could be calibrated when they have approached constant velocity or normal operation regime. In the case of pedestrian navigation, the small time during which ZUPTs (zero velocity updates) can be used to reduce effect of bias drifts can also be used to recalibrate the gyro bias, to realize long GPS-denied navigation capability. Provided with such capability, MEMS inertial sensors could truly revolutionize GPS denied navigation for soldiers and weapons, reducing loss of life due to misaim of weapons, and providing a degree of confidence in warfare obtained by knowing where one is at all times. GPS denied navigation is also important for commercial applications such as navigation inside buildings, and between tall buildings in urban environments, where GPS signals cannot be reached.
In the field of inertial sensors, a technique known as carouseling has been historically used to find north for gyro-compassing, and to calibrate the sensors at the same time. Carouseling requires the rotation of the inertial sensor about an axis by 180 degrees. By switching the direction of the gyroscope sensitive axis, the sensitivity of the gyroscope changes to negative of the value in the 180-degree off direction. The bias voltage does not typically change with the angle of orientation, and can be extracted from the two angle readings. The degree to which the bias can be removed depends on the degree to which the angle of rotation can be controlled. If the angle is in error by Δθ, then the error in measuring the rotation rate from the gyroscope can be comparable to the bias signal.
Existing carousels used in practice are too big and heavy to be considered for applications such as personal navigation and complementing GPS in automobiles. An insight is that the carousel can itself be made using miniature motion technology such as MEMS actuators themselves.
The inventor has recognized the benefits and advantages of being able to provides solutions to the problems outlined above, particularly by providing apparatus and methods enabling the measurement of distances with parts-per-billion (˜50-1000 ppb) accuracy (e.g., ≦5 nm position accuracy over a 100 mm dimensions; <1 arc-second precision angular position knowledge over 360 degree rotation) resulting in atomically stabilized and calibrated inertial sensors. Accelerometer bias (mg after calibration) of less than 0.01 and gyroscope bias (deg/hr after calibration) of less than 0.005 are anticipated to be achievable using the invention. It would be highly advantageous if all of these measurements could be performed in a package that is small (e.g., several cubic centimeters or less and consumes little power.
A MEMS carousel can be implemented in many ways as MEMS fabrication techniques can enable miniature rotating platforms or platforms that move in rectilinear motion on the surface of a chip. Thermal, electrostatic, or piezoelectric actuators, for example, can be used to move the platform.
Kohler et al. U.S. Pat. No. 7,066,004 discloses an inertial measurement unit using rotatable MEMS sensors. As disclosed therein, there is a desire within the art to incorporate MEM (microelectromechanical) inertial sensors into an inertial sensor system due to the potential size, weight, and cost savings. However, due to the relatively poor bias stability of currently available MEM inertial sensors (e.g. on the order of 50 degree/hr, this has not been possible in applications of sensor systems that require an accuracy greater than what currently available MEM sensors can provide. Poor bias stability, also referred to as drift, can lead to errors in the sensor's output, thus yielding errors in the calculated position, or calculated orientation, of a moving body to which the MEM inertial sensor is attached. The '004 patent describes a bias-compensated MEM inertial sensor, sensor system (inertial measurement unit (IMU)), and a method for bias error compensation of a sensor under a dynamic operating condition, in which means are provided for electrically assessing the MEM sensor. However, electrical means as disclosed, e.g., in the '004 patent, themselves contribute noise that prevents sufficient bias reduction or elimination for current and future applications.
Hence, even though it is feasible to make MEMS sensors onto miniature rotating platforms, it is very crucial to measure the position of the platform with high accuracy. Capacitive feedback on the sensor can provide position data but is prone to errors of electrode placement and movement due to substrate thermal expansion. These are the same sources of errors that induce the scale factor drift and biases in inertial sensors to begin with. One way to measure distances and motion accurately is to use optical wavefronts. Optical wavefronts can reflect from or transmit through structures and result in interference fields that can indicate the position of the motion of the structure. For example, a grating on a substrate will reflect a pattern that generates a diffraction pattern that is a Sin c function. A rectangular reflective grating on the rotor-chip will result in a Sin c(x) diffraction pattern at the imager with nodes placed at x=λz/g where λ is the wavelength, z is the gap between the aperture and the imager plane, and g is the grating period. For example, with z equal to 2 mm, λ=850 nm, and g=6 μm, the placement of the first diffraction node will be at x=0.28 mm showing up on the imager plane. The value of z can be estimated from knowing the value of g. Any tilt between the aperture chip and the imager chip can be quantified by the asymmetry of the diffraction pattern measured at the imager chip. As can be seen by the equation above, any changes in the optical wavelength can lead to changes in the pattern as well. If the optical wavelength is fixed, then the other variables are the system dimensions, which can be measured with as much uncertainty as there is in the wavelength stability. Atomic transitions with fixed optical wavelengths can be stable to parts in 1010. Such atomic transitions are used in the atomic clocks that interrogate hyperfine-transitions in atoms by lasers. Ready-made technology is available to enable a miniature atomically stable laser source, in the form of chip-scale atomic clocks, enabled by the combination of miniature VCSELs and miniature alkali metal vapor cells.
The inventors have recently used the stability of the wavelength to measure the position of a moving object attached to the camera. Co-owned U.S. application Ser. No. 13/062,832 entitled OPTICAL GRID FOR HIGH PRECISION AND HIGH RESOLUTION METHOD OF WAFER-SCALE NANOFABRICATION, the subject matter of which is incorporated herein by reference in its entirety, discloses a wafer-scale nano-metrology system for sensing position of a nanofabrication element using a Nano Optical Ruler Imaging System (NORIS) developed by the instant inventor. Further details about NORIS are described in Yoshimizu et al., Nanometrology optical ruler imaging system using diffraction from a quasiperiodic structure, OPTICS EXPRESS, Vol. 18, No. 20 (27 Sep. 2010)), the subject matter of which is incorporated herein by reference in its entirety.
Using NORIS and the stability of the laser, we can measure the position of the rotor with the inertial sensors. The rotor angle and offset are important for inertial sensor characterization, especially for gyro-compassing where the rotor will be rotated by 180 degrees and needs to be at a known angle within an arc-second to achieve ppm bias and scale-factor calculation. To measure the angle of the rotor to 1-arc-second, one must measure the edge-position of a 1 mm radius rotor with <4.84 nm accuracy. A change in the grating average position would translate into a change in the position of the diffraction pattern on the imager, spread over several pixels. By interpolation, the effective resolution of the angle measurement can be very high. One can approximate the measured diffraction patterns with base functions such as polynomials, and cubic splines. The truncation error between the function y=f(x) and the interpolating polynomial y=Pn(x) between (n+1) data points is proportional to the remainder polynomial of the (n+1)th order:
                                    f          ⁡                      (            x            )                          -                              P            n                    ⁡                      (            x            )                                      ≤                            M                      n            +            1                                                (                          n              +              1                        )                    !                    ⁢                                            (                          x              -                              x                l                                      )                    ⁢                      (                          x              -                              x                2                                      )                    ⁢                                          ⁢          …          ⁢                                          ⁢                      (                          x              -                              x                n                                      )                    ⁢                      (                          x              -                              x                                  n                  +                  1                                                      )                                        ,          ⁢      max                  M                  n          +          1                    =                        x          1                <        x        <                              x                          n              +              1                                ⁢                                                                f                                  (                                      n                    +                    1                                    )                                            ⁡                              (                x                )                                                                    
Here Mn+1 is the maximum magnitude of the n+1th derivative of f(x). If the data points are equally spaced with constant step size h, this being the pixel size in the imager, then the local error of the polynomial interpolation en(x)=|f(x)−Pn(x)| is bounded as:
                        f        ⁡                  (          x          )                    -                        P          n                ⁡                  (          x          )                          ≤                    M                  n          +          1                            4        ⁢                  (                      n            +            1                    )                      *          h              n        +        1            
The error decreases if the step size h becomes smaller with a fixed number of data points (n+1). For a typical diffraction pattern such as f(x)=Sin c(kx), the nth derivative at a null point (kx=π) is
                    ⅆ        n            ⁢              (                              Sin            ⁡                          (              kx              )                                /          kx                )                            ⅆ        n            ⁢      x        =                    n        ⁡                  (                      k            π                    )                    n        .  Using λ=850 nm, g=2 μm, and z=2 mm yields the peak error for a 10th order polynomial to be less than 10−10. The error in position determination from interpolation can be approximated by
            x      error        =                                                f            ⁡                          (              x              )                                -                                    P              n                        ⁡                          (              x              )                                                                    ⅆ          f                          ⅆ          x                      ,and the error is <1 nm even with a five-degree polynomial fit. Hence, very few exposed pixels are needed to accurately determine the position of the rotor. The resolution of precision of position can also be limited by the number of digital bits used to represent the pixel intensity. This error can be reduced greatly by interpolation and averaging over time with different thresholds for the analog to digital converter.
In addition to knowing the position of the rotor on which the inertial sensor is attached to, it is also possible to read the inertial sensors optically. There have been many implementations of optical readout of motion optically. These methods include interferometric techniques that require precise alignment. Other methods include gratings, in which case the wavelength is not stabilized. In the specific field of inertial sensors there have been attempts to realize optically readout of the proof masks. These techniques have led to the realization that even though the sensors can be made, the long term stability of the sensors suffers much like other miniature inertial sensors, due to drifts in gaps, and no independent standard of nature used to measure these changes.
In addition to measuring motion on the platforms, it is also possible to measure the dimensions of the devices being imaged by interpolating the pattern measured by the imager. In this mode of operation, the stable laser device structure allows in-situ measurement of gaps, masses, and orientation. These measurements can be used in advanced analytical modeling of device performance that can predict the sensitivity and the bias based on learning models. Thus long term stable measurement of a few devices parameters with built in metrology may enable correction of sensor performance.